Observer-invariant time derivatives on moving surfaces

2020/07/02 by Nitschke, Ingo, Voigt, Axel · 1 citation
#37C10 #53A05 #53A45 #70G45 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2007.01177

Abstract

Observer-invariance is regarded as a minimum requirement for an appropriate definition and derived systematically from a spacetime setting, where observer-invariance is a special case of a covariance principle and covered by Ricci-calculus. The analysis is considered for tangential n-tensor fields on moving surfaces and provides formulations which are applicable for computations. For various special cases, e.g., vector fields (n = 1) and symmetric and trace-less tensor fields (n = 2) we compare material and convected derivatives and demonstrate the different underlying physics.

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